Non-stationary Operating Research Articles

Vibration source inversion-based fault diagnosis: approach and application

The gear transmission system of industrial equipment is characterized by a highly integrated structure, non-stationary operating conditions, and large loads. Therefore, the attenuation of fault signal characteristics and the complexity of operating conditions in gear transmission systems significantly affect the effectiveness of vibration signal-based fault diagnosis. This paper proposes a unified diagnostic framework based on vibration source inversion for two typical transmission component fault signal phenomena: meshing frequency modulation sidebands and equally spaced fault characteristic frequency interval harmonic clusters. This approach incorporates the vibration transfer path analysis of passive subsystems and identifies bearing dynamic forces, followed by their decomposition, reconstruction, and sensitive frequency band localization. It enables accurate diagnosis of complex gear transmission systems under non-stationary conditions with limited vibration testing. The effectiveness and advantages of this method over existing mainstream signal processing techniques are validated through actual cases of gear and weak bearing fault diagnosis on a complex planetary gear transmission system test bench.

Identification of flame transfer functions during transient operation

Predicting thermoacoustic instabilities requires knowledge of the flame response to acoustic perturbations, which is characterized by the Impulse Response Function. Obtaining stability maps across an extensive parameter space is prohibitively costly with existing methods, both experimentally and numerically, as the data records must be obtained independently for each stationary operating condition. To address this problem, a nonparametric identification technique that enables the characterization of instantaneous Flame Transfer Functions (FTFs) under nonstationary operating conditions, based on a series expansion of the time-varying impulse response function (TV-IRF), is proposed. The technique is a direct extension of the Wiener-Hopf equation to nonstationary signals, yielding the linear minimum mean squared error estimator (LMMSEE) of the TV-IRF. This method is applied to data obtained from a model of a premixed, hydrogen-enriched swirl flame. It's hydrogen power fraction is rapidly varied from 12-43% over 100 milliseconds and the flame response to a band-limited, white-noise signal is computed. From the resulting input-output data, the TV-IRF is accurately estimated and the FTF for all hydrogen power fractions is obtained from a single data record. This method paves the way for cost-effective estimation of a map of FTF's from computational or experimental data, significantly reducing expenses in both cases.

The condition monitoring scheme for industrial IoT scenario: A distributed modeling for high-dimensional nonstationary data

Based on large-scale data collection and high-speed transmission, Industrial Internet of Things (IIoT) promotes the rapid development of intelligent manufacturing. IIoT systems are usually disturbed by complex external factors, which lead to high-dimensional nonstationary operating data. Besides, unexpected data transmission interruptions, sensor failures, and network delays lead to data loss. This paper proposes a distribution & communication strategy for monitoring high-dimensional nonstationary processes with missing values in IIoT scenarios. First, a deep learning-based imputation network is proposed to impute the missing values. Then a decomposition strategy based on degree of cointegration is proposed, which decomposes a high-dimensional nonstationary process into multiple blocks. And a communication strategy is proposed to mine the internal relationship between different blocks. Finally, faulty information is detected by a distributed framework. Two real cases from IIoT are applied to illustrate the monitoring performance of the proposed method. The results show that the proposed method outperforms existing benchmarks in data imputation and monitoring performance.

Dynamic time warping based instantaneous frequency estimation for rotating machineries under non-stationary operating conditions

Abstract For tacho-less order tracking, it is crucial to achieve an accurate estimation of instantaneous phase and frequency under non-stationary conditions for fault diagnosis of mechanical systems. Therefore, an instantaneous frequency estimation method based on dynamic time warping for rotating machinery was proposed. Firstly, a mono-component signal is obtained by variational mode decomposition of multi-harmonic vibration signal generated in practical engineering. Then, a stationary reference signal is constructed by the mean frequency of the vibration signal, which is obtained by the signal spectrum. Aligning the vibration signal with the reference signal to obtain the rough phase estimation and warping path. Finally, a polynomial model is constructed to calculate the analytic expression of the smooth warping path to obtain the instantaneous frequency result. The simulation and experiment present that the dynamic time warping-based method can estimate the instantaneous frequency of the signal under non-stationary conditions. Compared with the classical Hilbert transform method, the proposed dynamic time-warping algorithm has stronger noise resistance.

Real-time AIoT anomaly detection for industrial diesel generator based an efficient deep learning CNN-LSTM in industry 4.0

Anomaly detection for industrial diesel generators, in which unexpected faults could lead to severe consequences, is still challenged due to their complex structure and nonstationary operation. Maintenance engineers who manually audit diesel generators for anomaly detection require significant expertise and knowledge. This study proposes a real-time intelligent AIoT system-based convolution neural network long short-term memory (CNN-LSTM) to enhance efficiency and decrease labor costs of industrial diesel generator maintenance service. The AIoT system could autonomously classify abnormal conditions of industrial diesel generators through supervised learning techniques. Several anomaly failure conditions are identified by maintenance experts and are simulated in the laboratory to collect the working parameters based on developed IoT modules. Pearson product-moment coefficients are computed to effectively evaluate the interdependence between collected variables and the target anomaly types. The proposed CNN-LSTM structure is hyperparameter fine-tuning for identifying the most critical configurations in failure-diagnosing applications. The developed approach is comprehensively analyzed and evaluated with other state-of-the-art individual deep learning algorithms, including recurrent neural network (RNN), LSTM, gate-recurrent unit (GRU), and CNN. The experiment results indicate that the proposed hybrid CNN-LSTM could achieve distinguished diagnosis precision of anomaly conditions of industrial diesel generators and significantly improve the classified performance in Industry 4.0.

ANALYSIS OF PROPYLENE GLYCOL/ETHYLENE GLYCOL HEATING IN THE CYLINDRICAL CHANNEL OF THE SOLAR HEAT COLLECTOR

When designing solar thermal collectors, non-stationary operating conditions of the solar system are considered to determine the instantaneous heat output and temperature of the heat carriers during a given day or period. It is known that the amount of useful heat absorbed by a solar thermal collector is directly dependent on the temperature of the heat carrier at the inlet and outlet of the solar thermal collector. The calculation of the heat consumption and/or storage system also requires the temperature of the heat carrier at the outlet of the solar collector. The heating of the heat carrier in a solar collector can be divided into two stages: heating of the walls of the heat exchanger (cylindrical channel) in a solar thermal collector by solar energy and heating of propylene glycol/ethylene glycol in the heat exchanger (cylindrical channel) of a solar thermal collector. This paper presents seven methods for determining the temperature field of the walls of the heat exchanger (cylindrical channel) of a solar thermal collector, depending on the initial and boundary conditions. The most general case for calculating the temperature field of propylene glycol/ethylene glycol moving in the heat exchanger of a solar heat collector assumes the presence of heat exchange on the surfaces of its contact with the walls of the cylindrical channel and with the environment. The calculation takes into account the difficulties associated with the significant nonlinearity of boundary conditions of the "given surface radiation" type. That is, it is taken into account that one surface of the heat exchanger channel is turned to solar radiation, and the opposite is turned to the back wall of the solar heat collector. The solution is found analytically using the method of Green's functions.

Nonlinear modeling for bearing fault diagnosis in non-stationary operating conditions

Nonlinear modeling for bearing fault diagnosis in non-stationary operating conditions

Experimental validation of a short-term damping estimation method for wind turbines in nonstationary operating conditions

Abstract. Modal properties and especially damping of operational wind turbines can vary over short time periods as a consequence of environmental and operational variability. This study seeks to experimentally test and validate a recently proposed method for short-term damping and natural frequency estimation of structures under the influence of varying environmental and operational conditions from measured vibration responses. The method is based on Gaussian process time-dependent auto-regressive moving average (GP-TARMA) modelling and is tested via two applications: a laboratory three-storey shear frame structure with controllable, time-varying damping and a flutter test of a full-scale 7 MW wind turbine prototype, in which two edgewise modes become unstable. Damping estimates for the shear frame compare well with estimates obtained with stochastic subspace identification (SSI) and standard impact hammer tests. The efficacy of the GP-TARMA approach for short-term damping estimation is illustrated through comparison to short-term SSI estimates. For the full-scale flutter test, GP-TARMA model residuals imply that the model cannot be expected to be entirely accurate. However, the damping estimates are physically meaningful and compare well with a previous study. The study shows that the GP-TARMA approach is an effective method for short-term damping estimation from vibration response measurements, given that there are enough training data and that there is a representative model structure.

Rotating Machinery Fault Diagnosis under Time–Varying Speed Conditions Based on Adaptive Identification of Order Structure

Rotating machinery fault diagnosis is of key significance for ensuring safe and efficient operation of various industrial equipment. However, under nonstationary operating conditions, the fault–induced characteristic frequencies are often time–varying. Conventional Fourier spectrum analysis is not suitable for revealing time–varying details, and nonstationary fault feature extraction methods are still in desperate need. Order spectrum can reveal the rotational–speed–related time–varying frequency components as spectral peaks in order domain, thus facilitating fault feature extraction under time–varying speed conditions. However, the speed–unrelated frequency components are still nonstationary after angular–domain resampling, thus causing wide–band features and interferences in the order spectrum. To overcome such a drawback, this work proposes a rotating machinery fault diagnosis method based on adaptive separation of time–varying components and order feature extraction. Firstly, the rotational speed is estimated by the multi–order probabilistic approach (MOPA), thus eliminating the inconvenience of installing measurement equipment. Secondly, adaptive separation of the time–varying frequency component is achieved through time–varying filtering and surrogate test. It effectively eliminates interference from irrelevant components and noise. Finally, a high–resolution order spectrum is constructed based on the average amplitude envelope of each mono–component. It does not involve Fourier transform or angular–domain resampling, thus avoiding spectral leakage and resampling errors. By identifying the fault–related spectral peaks in the constructed order spectrum, accurate fault diagnosis can be achieved. The Rényi entropy values of the proposed order spectrum are significantly lower than those of the traditional order spectrum. This result verifies the effective energy concentration and high resolution of the proposed order spectrum. The results of both numerical simulation and lab experiments confirm the effectiveness of the proposed method in accurately presenting the time–varying frequency components for rotating machinery diagnosing faults.

Compound fault diagnosis of rolling bearings based on AVMD and IMOMEDA

The intricate nature of compound fault diagnosis in rolling bearings during nonstationary operations poses a challenge. To address this, a novel technique combines adaptive variational mode decomposition (AVMD) with improved multipoint optimal minimum entropy deconvolution adjustment (IMOMEDA). The compound fault signal is isolated through AVMD, with internal parameters obtained via a new indicator termed integrated fault-impact measure index guiding the improved dung beetle optimizer. An adaptive selection method, using a weight factor, chooses the intrinsic mode function containing principal fault data. IMOMEDA whose key parameters are determined by a novel combinatorial strategy is then employed to deconvolute selected fault components, enhancing periodic fault impulses by removing complex interferences and ambient noise. The deconvoluted signal undergoes enhanced envelope spectrum processing to extract fault frequencies and identify fault types. Numerical simulations and experimental data confirm the method’s effectiveness and feasibility for compound faults diagnosis of rolling bearings, showcasing its superiority over existing techniques.

Event-Triggered Relearning Modeling Method for Stochastic System with Non-Stationary Variable Operating Conditions

This study presents a novel event-triggered relearning framework for neural network modeling, designed to improve prediction precision in dynamic stochastic complex industrial systems under non-stationary and variable conditions. Firstly, a sliding window algorithm combined with entropy is applied to divide the input and output datasets across different operational conditions, establishing clear data boundaries. Following this, the prediction errors derived from the neural network under different operational states are harnessed to define a set of event-triggered relearning criteria. Once these conditions are triggered, the relevant dataset is used to recalibrate the model to the specific operational condition and predict the data under this operating condition. When the predicted data fall within the training input range of a pre-trained model, we switch to that model for immediate prediction. Compared with the conventional BP neural network model and random vector functional-link network, the proposed model can produce a better estimation accuracy and reduce computation costs. Finally, the effectiveness of our proposed method is validated through numerical simulation tests using nonlinear Hammerstein models with Gaussian noise, reflecting complex stochastic industrial processes.

Frequency bearing fault detection in non-stationary state operation of induction motors using hybrid approach based on wavelet transforms and pencil matrix

Frequency bearing fault detection in non-stationary state operation of induction motors using hybrid approach based on wavelet transforms and pencil matrix

Modeling of the removal of combustion products in the pipe of a low-rise building as a control object

The features of the formation and methods of preventing condensation in the chimney of an apartment low-rise building with an individual decentralized heat supply system are considered. A mathematical model of the technological process of removing flue gases from gas boilers in an apartment building through a collective chimney pipe as a multidimensional control object with distributed parameters, which is understood as a set of thermophysical processes occurring during the removal of combustion products. Numerical simulation of a collective chimney pipe is performed on the example of a three-storey apartment building with gas boilers installed in each apartment as a control object. A method of step-by-step experiments is proposed. At the first stage, the dependences of the distribution of the temperature field inside the chimney during non-stationary operation of boilers and changing ambient temperature are obtained. The phenomenon of condensate occurrence has been confirmed experimentally, and the most characteristic areas subject to its occurrence have been identified. During the second stage of research, it was found that it is most effective and economically feasible to prevent the formation of condensate by using a heating cable in the attic and chimney head sections. It is shown that the change of control actions has an effect on the temperature of adjacent sections of the chimney. The revealed non-stationarity is taken into account by inter-channel connections through the object in the block diagram. It is proved that, in relation to solving the problem of removing combustion products from the chimney, an object with distributed parameters can be represented by a model with concentrated parameters, for which the structure is synthesized and proper operators and operators of inter-channel connections are found in the form of transfer functions with variable parameters. The resulting model is problem-oriented to create a two-dimensional automatic temperature control system on the inner surface of the chimney in order to prevent the formation of condensate in the pipe.

Extremely compact and lightweight triboelectric nanogenerator for spacecraft flywheel system health monitoring

The abnormal state of supporting bearings significantly affects the directional accuracy of spacecraft flywheel systems. A self-sensing triboelectric nanogenerator (TENG) offers a desirable route for on-orbit health monitoring and can potentially improve the intelligence level of spacecraft. Here, an extremely compact and lightweight TENG (CL-TENG) for the nonguided clearance of bearings is proposed and fabricated for the condition monitoring of a flywheel assembly. Using the bearing radial space allows the CL-TENG to perceive the revolution and whirling behavior of the cage; therefore, the output of the CL-TENG is simultaneously affected by the bearing speed and load. A test platform for capturing the kinematic of the cage is established to validate the effectiveness of the CL-TENG based on bearing skidding, cage rotation, and whirling instability. A negative exponential correlation between the output voltage and dynamic whirling clearance index is shown to be the basis of cage whirling sensing. The internal clearance and materials of the CL-TENG are optimized to enhance the output performance while preventing wear on the flexible electrodes. The application of the CL-TENG to an actual flywheel system in a simulated space environment and nonstationary operating conditions demonstrate its advantages in detecting the abnormal operating state of the cage.

Dynamic misalignment effects on performance of dynamically loaded journal bearings

The lubrication characteristics of dynamically loaded journal bearings are significantly affected by misalignments. However, existing research on misalignment primarily focuses on fixed misalignment models, and studies on the nonlinear dynamic response of dynamically loaded bearings under dynamic misalignment are yet to be reported. To address this research gap, this study proposed a dynamic misalignment model coupled with rotor dynamics and transient mixed elastohydrodynamic lubrication. The model comprehensively considers factors such as journal eccentric translation, surface topography, oil film cavitation, and bearing elastic deformation. Upon model validation, numerical simulations are conducted to reveal the single-cycle nonlinear tribological characteristics of dynamically loaded bearings subjected to transient time-varying dynamic loads and time-varying misalignment moments. Based on the dynamic misalignment model, a series of parameter studies were conducted to explore the influence of operating conditions such as load magnitude and rotational speed on lubrication characteristics. The research also evaluated the impact of various structural parameters, including surface roughness, bearing bush thickness, and radial clearance, on the performance of dynamically loaded bearings. The numerical results indicate that the impact of fixed-value misalignment on the performance is highly dependent on the manually set deflection angles. Under light-load and high-speed nonstationary operating conditions, the effect of dynamic misalignment on the lubrication characteristics of dynamically loaded journal bearings was significantly amplified. Furthermore, a smoother surface, thicker bearing bush, and smaller radial clearance intensify dynamic misalignment's influence, compared to fixed-value misalignment, on the transient rough contact behavior at the interface. The findings of this study provide valuable guidance and references for the theoretical analysis and optimization design of dynamically loaded journal bearings.

Short-term damping estimation for time-varying vibrating structures in nonstationary operating conditions

Various structures exhibit time-varying modal properties driven by short-term variability of environmental and operational conditions, which can cause considerable short-term variations in the modal characteristics, and modal damping, in particular. This study focuses on short-term damping estimation based on operational response measurements, for which a Gaussian process time-dependent auto-regressive moving average time series model is proposed. The model coefficients are represented by basis functions which express dependence on influencing environmental and operational variables, to account for various phenomena driving the time-varying nature of the modal characteristics. The method is verified by estimating short-term damping from the response of a simulated two-mode model. The applicability of the method for more complex cases is demonstrated by estimating the short-term damping of a multi-megawatt wind turbine in operation (and during an extreme wind gust) by means of its simulated edgewise blade response. The results demonstrate that the proposed method offers an enabling approach towards short-term damping and natural frequency estimation based on response measurements.

Feasibility Analysis of Online Uncertainty Metrics for PMU-Based State Estimation

The ever-increasing penetration of renewable energy sources and distributed generation needs developing and deploying more sophisticated and precise control techniques. The paradigm shift from high-rotational inertia towards inverter-connected facilities has made modern power systems subject to strongly non-stationary operating conditions. In this context, phasor measurement units (PMUs) represent a promising solution due to their accuracy and time synchronization. The current paper further develops the concepts recently published proposing performance assessment of PMUs relying on metrics specifically defined to quantify the estimation accuracy, reporting latency, and response time. Our focus is on determining the confidence interval associated with these metrics and thus derive a robust approach for their application in measurement-based network controlling efforts. The configuration of the used simulation model is detailed, and the state estimation results as a function of the selected measurement weighing criteria are presented, concluding as a possible application of the reliability metrics in Weighted Least Squares and Discrete Kalman Filter state estimators, highlighting the performance enhancement as well as the theoretical limits of the proposed approach.

Вплив шорсткості поверхні камери енергетичної установки на низькочас-тотні автоколивання холодного робочого газу

Dynamic processes in the combustion chamber have a significant effect on the characteristics of the working processes of solid-propellant rocket engines (LPREs). Pressure jumps and a sharp increase in the local temperature of the combustion products in non-stationary engine operation modes can lead to overrating values of operating parameters and a failure of the LPRE combustion chamber structure. The dynamic processes in the LPRE combustion chamber develop in a complex interconnection of a large number of physical and chemical processes that occur in the gas-dynamic part of the working space of the engine chamber and often lead to self-oscillating modes of engine operation. This is evidenced by numerous data on LPRE fire tests. This paper presents the results of a numerical study of the effect of the LPRE chamber inner surface roughness on LPRE operating parameter low-frequency self-oscillations. The study was made using up-to-date computer simulation means and analysis. Low-frequency (up to 1,000 Hz) oscillations in an LPRE combustion chamber were studied for a power plant test chamber in cold operation with the use of two different approaches to numerical modeling of the dynamics of in-chamber processes: the development and study of a 3D model of the dynamic system of combustion chamber structure – combustion products using the finite element method and the development and study of an axisymmetric 2D model of engine chamber gas flow using the finite volume method. The study revealed a self-oscillatory flow regime caused by combustion product vorticity and acoustic feedback due to vortices colliding with the chamber components or the LPRE nozzle. It was shown that accounting for the wall roughness increased gas vorticity in the gas–solid dynamic interaction zone and the chamber gas oscillation amplitude (on the average, by a factor of 2.5 at a maximum wall roughness height of 56 ?m). The calculated gas flow pattern in the vorticity zones of the chamber and the low-frequency gas pressure oscillation parameters are in qualitative agreement with the experimental ones.

Intelligent Fault Diagnosis of Robotic Strain Wave Gear Reducer Using Area-Metric-Based Sampling

The main challenge with rotating machine fault diagnosis is the condition monitoring of machines undergoing nonstationary operations. One possible way of efficiently handling this situation is to use the deep learning (DL) method. However, most DL methods have difficulties when the issue of imbalanced datasets occurs. This paper proposes a novel framework to mitigate this issue by developing an area-metric-based sampling method. In the proposed process, the new sampling scheme can identify which locations of the datasets can potentially have a high degree of surprise. The basic idea of the proposed method is whenever significant deviations from the area metrics are observed to populate more sample points. In addition, to improve the training accuracy of the DL method, the obtained sampled datasets are transformed into a continuous wavelet transform (CWT)-based scalogram representing the time–frequency component. The dilated convolutional neural network (CNN) is also introduced as a classification process with the altered images. The efficacy of the proposed method is demonstrated with fault diagnosis problems for welding robots. The obtained results are also compared with existing methods.

A Hydraulic Axial Piston Pump Fault Diagnosis Based on Instantaneous Angular Speed under Non-Stationary Conditions

Due to the intense noise interference in hydraulic systems, it is extremely difficult to detect component faults through vibration signals. Diagnostic performance is also constrained by highly time-varying and non-stationary operating conditions. This study proposes to use instantaneous angular speed (IAS) signals that are both operational and state parameters as sources of information. Firstly, the instantaneous angular speed fluctuation (IASF) of a piston pump is analyzed theoretically, and it is concluded that its fluctuating components contain the health status information of the components. The IASF can then be obtained by subtracting the speed trend term from IAS signals obtained via a magneto-electric speed sensor. A synchro-extraction of the normal S transform (SNST) is proposed to process it via line-pass filtering. Finally, the filtered and reconstructed IASF signal is utilized to draw a two-dimensional polar coordinate map online. A non-stationary-condition test is carried out on the test platform to monitor the morphological characteristics of the valve plate under normal, slight, and severe wear conditions. The polar plot shows significant increases in speed fluctuations and oscillation times within a range from 180° to 270°. The relevant research results reflect that the IAS signal can provide a new method for monitoring the operating status of and conducting fault diagnoses for hydraulic equipment.